Modelling Biomolecular Structures in Categorical Systems Theory

In the systemic movement there exist numerous approaches to systems, the most profound of which is the theory of functional systems by Anokhin, which remained largely intuitive science until his pioneering works. The basic principles of functional systems are formalized with the help of the convolutional polycategories in the form of categorical systems theory, which embraced the main systemic approaches, including the traditional mathematical theory of systems. Convolutional polycategories can be built using categorical splices that directly model the external and internal parts of systems. For an algebraic biology using the categorical theory of systems in relation to systemic constructions, the main task of which is to predict the properties of organisms from the genome using strict algebraic methods, new categorical methods are proposed that are widely used in categorical systems theory. These methods are based on the theory of categorical splices, with the help of which the behaviour of quantum-mechanical particles is modelled, in particular, within the framework of the proposed representation of molecules, including RNA and DNA, as categorical systems. Thus, new algebraic and categorical methods (associative algebras with identities, PROP, categorical splices) are involved in the analysis of the genome. The paper presents new results on these matters.